Broadcasting on [0, L]

0 on [ L ] - Homotopy Groups

The paper is devoted to investigation of some properties of [L]-homotopy groups. It is proved, in particular, that for any finite CW -complex L, satisfying double inequality [S] < [L] ≤ [S], π [L] n (S) = Z. Here [L] denotes extension type of complex L and π [L] n (X) denotes n-th [L]-homotopy group of X .

0 0 T L 0 0 0 7 . -| |

Broadcasting on cactus graphs

Broadcasting is the process of dissemination of a message from one vertex (called originator) to all other vertices in the graph. This task is accomplished by placing a sequence of calls between neighboring vertices, where one call requires one unit of time and each call involves exactly two vertices. Each vertex can participate in one call per one unit of time. Determination of the broadcast t...

Broadcasting on Faulty Hypercubes

In this paper we propose a method for constructing the maximum number of edge-disjoint spanning trees (in the directed sense) on a hypercube with arbitrary one faulty node. Each spanning tree is of optimal height. By taking the common neighbor of the roots of these edge-disjoint spanning trees as the new root and reversing the direction of the directed link from each root to the new root, a spa...

The Geometry of L 0

Suppose that we have the unit Euclidean ball in R and construct new bodies using three operations linear transformations, closure in the radial metric and multiplicative summation defined by ‖x‖K+0L = p ‖x‖K‖x‖L. We prove that in dimension 3 this procedure gives all origin symmetric convex bodies, while this is no longer true in dimensions 4 and higher. We introduce the concept of embedding of ...